Dual Identity in Repressive Contexts: An Agent-Based Model of Protest Dynamics

Abstract

Protest campaign movements are often carried out by coalitions rather than by homogeneous groups. Accordingly, an opposition member has both a narrow partisan identity and a broad all-opposition identity. Seeking to prevent mass political participation, autocracies can repress protesters regardless of their group membership or apply the “divide and conquer” principle, targeting specific groups. Any strategy of repression drives some dynamics of identity. For instance, broad repression may rally the opposition by increasing broad identity at the expense of narrow identity. This dynamic of identity causes complex dynamics of motivation for participation in the protest, which affects the turnout. The paper introduces a computational model to describe the dynamics of the turnout. The model employs the social identity model of collective action (SIMCA) and accounts for the dual protest identity.

Keywords

political protest political mobilization agent-based model computational social science decision-making

Introduction

Modern opposition movements do not represent a single political force but consist of distinct groups with different values, social status, ideological orientations, and formal and informal organizational patterns. Large-scale revolutions of the 21st century, such as the Orange Revolution (2004–2005) and Euromaidan (2013–2014) in Ukraine, the Rose Revolution (2003–2004) in Georgia, the Tulip Revolution (2005) in Kyrgyzstan, the Cedar Revolution (2005) in Lebanon, and the Saffron Revolution (2007) in Myanmar, together with the vast majority of anti-government protests during the Arab Spring (2010–2014), appeared to be extremely heterogeneous in their social and political composition. The formation of broad coalitions and bridging group boundaries is one of the key factors in the massive turnout for street protests, which, in turn, ultimately determines the success of opposition movements.

Non-democracies, for their part, seek to prevent broad political participation. Although they sometimes use nonviolent strategies such as concession or accommodation, repression remains the most widely used tool to inhibit street protest (Fujikawa, 2017; Rasler, 1996). The social heterogeneity of protest movements not only threatens such regimes but also provides opportunities for the autocrats to remain in power. Along with the use of broad (indiscriminate) repression, suppressing protesters regardless of their group membership, they can apply the “divide and conquer” principle, targeting specific groups within a broader movement.

Under what conditions will protests be more resilient—in terms of turnout—to both broad and targeted repression technologies? This question, central to our work, has not been systematically explored in modern political science. To date, we have only some episodic and case-specific evidence (see e.g., Lawrence (2017)). The general theoretical prediction, based on rational choice theory (Lichbach, 1987) and partly supported by game theoretic modeling (Pierskalla, 2010), is that any repression should have a monotonically negative effect on protest participation by increasing its costs. This prediction, however, runs into very conflicting empirical evidence. Some studies show that repression decreases protest (Gupta et al., 1993; Steinert-Threlkeld & Steinert-Threlkeld, 2021; Steinert-Threlkeld, 2017), while others show it increases protest (Ayanian & Tausch, 2016; Bell & Murdie, 2018). Some research supports curvilinear relationships: at times u-shaped (Opp & Roehl, 1990; Rasler, 1996) and others n-shaped (Muller, 1985; Schock, 1999). Moreover, sometimes studies even find the complete absence of a significant effect (Bischof & Fink, 2015). This issue, often referred to as a “protest–repression nexus” or “repression–dissent puzzle,” still remains unresolved (for a comprehensive review, see Steinert-Threlkeld and Steinert-Threlkeld (2021)).

Some of the roots of this puzzle can be found in the very definition of repression. The one most commonly accepted among political scholars belongs to Davenport (2005: 122), “Actions taken by authorities against individuals and/or groups within their territorial jurisdiction that either restrict the behavior and/or beliefs of citizens through the imposition of negative sanctions (e.g., applying curfews, conducting mass arrests, and banning political organizations) or that physically damage or eliminate citizens through the violation of personal integrity (e.g., using torture, disappearances, and mass killing).” In this definition, given from a macro perspective, the focus is placed on the central authority. Much less attention is paid to the micro-level: personal perceptions and experiences of repression, their influence on the motivation to protest (Honari, 2018). In the literature review, we will show that such a bias is also typical for related agent-based modeling.

In the model presented in this paper, we concentrate on the micro-level effects of repression on motivational mechanism, understood through the lens of group-level (both inter- and intra-) dynamics. The latter focus is necessary because we strive to explain the group-based repression strategy.

Our guiding methodology in achieving this goal is a social identity approach (SIA) in both of its major components—social identity theory (SIT) (Klandermans, 1997; Tajfel & Turner, 1979) and self-categorization theory (SCT) (Turner, 1985). We rely on it for several important reasons.

Firstly, social identity—a person’s sense of who they are based on their group membership (opposition in our case)—is itself a driver of protest participation (Klandermans et al., 2002). Our model considers social identity as a dynamic variable driven by repression, and that affects the protest turnout. One may say that an individual becomes “more social” when their group is exposed to repression.

Secondly, it has recently been argued that it is not a mere protest identity but multiple identities that bear explanatory power (González & Brown, 2003; Van Stekelenburg & Klandermans, 2017). Moreover, given the complex social composition of the protest movement, switching from a narrow identity with a specific dissent group to a broader identity with the opposition as a whole becomes a clue to the coalition formation process and the potential for mass protest participation. This idea has recently been applied to the protest–repression nexus by Nugent (2020). In her framework, repression is a shared experience for those subjected to it. Being a specifically traumatic experience, it ties people together by emphasizing their common attributes. Consequently, repression directed against all groups will contribute to the formation of a broad opposition identity. Targeted repression is expected to have the opposite effect. It will strengthen the identity of a certain opposition group. We rely primarily on Nugent’s (2020) experimental results to formalize and calibrate the impact of repression on identification dynamics in our model.

We focus mainly on the quantitative properties of identity. Following Huddy (2003), we argue that it is not group identity per se but its strength that influences group members’ readiness to act in terms of their group membership. In our model, each agent is characterized by parameters reflecting the degrees to which an individual demonstrates narrow and broad identity. The categories are not mutually exclusive and can be assigned values that reflect the current level of individual identification. These values change over time due to the influence of the repression applied. Thus, the situation-driven dynamics of personal dual identification vectors (DIVs) are at the core of the model introduced in this paper.

Finally (and importantly), SIA serves as an integrating framework for bringing together a complex set of motives for participating in protest activity. Protest mobilization is affected by perceived injustice according to relative deprivation theory (Gurr, 1970; Walker & Smith, 2002). Resource mobilization theory (Klandermans, 1984; Tilly, 1978) instead emphasizes the role of efficacy: people tend to participate if they think this will make their goals more achievable. SIA considers these approaches not as competing theories but as parts of a single framework for describing the motivational systems of individuals. A key step was made by Van Zomeren et al. (2008), who proposed the social identity model of collective action (SIMCA). SIMCA ties these theories together, showing that social identity motivates protest participation directly and indirectly via the mediation of anger and efficacy belief. That is, anger is not just a negative emotion but also a feeling of injustice on behalf of the group that an individual associates themselves with. Likewise, efficacy is more of a belief in the power of the group one associates with than a probabilistic assessment of the chances of success. This is especially true for politicized identities (Sturmer, Simon 2004), like the ones we consider here. Thus, the formalization of the general logic of SIMCA within the framework of agent-based modeling is our goal here.

Our computational experiments show, in the first place, that broad and targeted repression differs significantly in its impact on protest behavior. Targeted repression is unable to suppress protests. This is not surprising since there is no reason to be inactive for members of groups not being targeted. At the same time, broad repression can lead to the suppression of protests, especially when the average risk aversion of the population is high. However, if levels of risk aversion are low enough, no level of repression can guarantee suppression.

Secondly, our experiments demonstrate that repression can increase uncertainty as to protest turnout. Specifically, in real-life situations the parameters of the social system can be estimated only approximately, so in our model, individuals’ predispositions (attitudes) toward participation in the protest campaign are taken as having a stochastic component. These relatively small stochastic variations in attitudes may result in significant variation in turnout. This effect is shown to be specific to different types of repression. Under some combinations of parameters, small stochastic variation in attitudes leads to significant variation in turnout in the case of broad repression and to relatively small variation when repression is targeted. In other words, the use of broad repression increases uncertainty as to turnout, whereas targeted repression does not. However, under different combinations of parameters, targeted repression increases uncertainty, whereas broad repression does not.

Finally, we considered the effect of homophily on the outcome of protest campaigns. Here, homophily refers to the relative frequency of network connections between members of the same opposition group. We have found that (i) in the case of targeted repression, the level of homophily affects more the turnout of the survived campaigns than the chance that the campaign survives and (ii) in the case of broad repression, the level of homophily affects more the chance of surviving than the turnout of the survived campaigns. Here, the term “survival” means that the stationary turnout is not equal to zero. Namely, in some scenarios, the turnout decreases to zero due to repression, which means that the protest campaign does not survive. In other scenarios, the turnout tends to some positive constant (or, sometimes, the constant plus small oscillation). This constant represents the stationary turnout (see the description of the computational model below for technical details).

The rest of the paper is structured as follows. In the section The Related research, we discuss earlier agent-based models of the protest–repression nexus and demonstrate how we build on and advance this work. The section The Model introduces the model, and the section The Simulation Method outlines the setup of computational experiments. The section The Analytical Study of the Model studies the simplified version of the model analytically; the section The Simulations and Results describes the results of computational experiments. The section The Conclusion and Discussion summarizes the results and discusses the limitations of the study.

Related Research

Agent-based models of protest–repression interactions have been developed for at least two recent decades. The beginning was laid by Epstein’s (2002) seminal work “Civil Violence”; it gave rise to a whole family of successor models and remains very influential to this day. We also rely on some of its ideas and, at the same time, try to overcome the difficulties they generate; therefore, we will briefly discuss its basic design.

First, Epstein's citizen agents can be in one of two discrete states: “active” or “quiescent”; subsequently, such a solution has been implemented in almost all models of protest activity, including ours. Second, the transition from one state to another is guided by the balance of determinants pushing agents toward participation, on the one hand, and acting in the opposite direction, on the other. In Epstein’s model, the forces on the side of participation are grievances, which depend on individual hardships and the macro-level of the regime's legitimacy. The restraining factors are risk aversion and a contextual, dynamically changing probability of being arrested by law enforcement officers (or simply “cops'' in the author’s edition—another type of agent in the model). The agent-estimated arrest probability is a function of the “cop-to-active ratio” (the ratio of the number of police officers to the number of protesters) within her vision radius—the number of cellular lattice positions that the agent is able to inspect in the local environment. Risk aversion and estimated arrest probability together form the individual’s net risk, counterbalancing their intention to protest.

A natural solution to transform the continuous motivational balance into one of two discrete states—quiescent or active—is to use an activation threshold. If the difference between risks and grievances exceeds a certain value (zero in the simplest form), the agent switches to the active state, and vice versa.¹

In the later works, this design has undergone a number of modifications, such as including network ties instead (Lemos, 2018) or along with (Fonoberova et al., 2019) original cellular lattice, or making an agent’s grievances dependent on the difference between their profits and the average of their neighbors (Kim & Hanneman, 2011), or increasing the number of agent types by adding members of revolutionary organizations (Moro, 2016), etc. Yet, the two interrelated cornerstones of Epstein’s (2002) approach, namely, the motivational balance and the activation threshold, remain unchanged and relevant within this stream in agent-based modeling. We largely rely on them in the model presented in this paper.

At the same time, the effect of repression on protest behavior looks much less realistic in this approach. Police arrests of active citizens exclude them from the fields of vision of other agents for a certain period of time; it is called a “jail term.” This leads to an increase in the cop-to-active ratio, thus making it riskier for the remaining agents to participate. By affecting only one side of the motivational balance, this impact works only in one direction, reducing the turnout. Such an indirect and purely “mechanical” approach ignores any psychological effects of repression, like possible outbursts of anger leading to backlash to state violence.² The importance of the latter for real-life protests has been demonstrated by many studies (see, e.g., Ayanian & Tausch, 2016; Ayanian et al., 2021).

One solution to this problem has been proposed within another strand of protest–repression modeling, framed by influential works of Siegel (2009, 2011) and, most recently, Steinert-Threlkeld and Steinert-Threlkeld (2021). These studies concentrate primarily on social influence—the impact of individuals’ network environments on their decisions to take part in collective action. This focus leads to significant differences in the basic design of such models compared to Epstein’s. The most important of these is the explicit distinction between personal and external motivation (Siegel, 2009). The former is the constant result of many factors related to one’s desire to participate—like moral certainty of the cause, or being unemployed, or dissatisfaction with the political system—that do not depend on the participation of others. The latter, on the contrary, is the context-dependent response to the behavior of others in the network: the more people connected with the individual participate in the protest, the more she herself is motivated to participate. This logic is in line with the social contagion approach, which has a long tradition in agent-based modeling (Centola & Macy, 2007; Watts, 2002; Piedrahita et al., 2018).

The effect of repression is modeled within this framework in two ways. The baseline approach is to remove a certain proportion of active agents (which actually reproduces Epstein’s solution), and, again as in Epstein’s model, this is a one-way effect, leading to lower turnout rates by eliminating the direct participation of the protesters and by reducing the external motivations of the rest (Steinert-Threlkeld & Steinert-Threlkeld, 2021). The more sophisticated approach proposed by Siegel (2011) adds two psychological responses from the peers of repressed agents to their technical withdrawal: anger and fear. Anger is implemented via a positive incentive to participate, added to an individual’s internal motivation; fear is modeled similarly, but the incentive gets a negative sign.

This solution is an important step forward in protest–repression modeling. This solution, however, has one serious disadvantage. It means that two different model specifications are needed, along with two different computational experiments. Yet, in reality, these bidirectional effects act simultaneously, and the solution of the protest–repression puzzle may not be completely reliable without explicitly taking this fact into account. In this paper, we propose such a technique. It is based on a combination of Epstein’s (2002) motivational balance and Siegel’s (2011) ambivalent psychological effect of repression. In our design, repression affects both sides of the motivational balance concurrently, stimulating participation through anger and deterring it through increased risk.

To model realistically such complex cognitive processes, one needs to be based on the developed and empirically supported socio-psychological theory of protest activity. These requirements are best met by SIMCA (van Zomeren et al., 2008), which we have briefly described in the introduction. Most importantly, it provides an opportunity to link heterogeneous incentives together in one common framework based on social identity. As an independent motive, social identity connects the effects of anger and efficacy belief in a way that provides clear guidelines for model building.

Surprisingly, we failed to find convincing attempts to formalize SIMCA in the literature, at least in the context of contentious politics. Moreover, very few formal models of protest activity include social identity in any form. One example is the already cited work of Kim and Hanneman (2011), which examines the influence of group identification—together with inequalities in wage distribution—on the frequency, strength, and duration of protest outbreaks. In the model, this effect is mediated by risk aversion: the protesters surrounded mostly by in-group members are more risk-taking, and more risk-averse otherwise. The authors show that group identification does not strongly affect the frequency of local uprisings, but it negatively influences their intensity and duration.

In the neighboring area of system dynamics, an attractive approach to base the model on the principles of social identity theory belongs to Salimi et al. (2022). Though this work focuses on large-scale changes in social norms and does not directly address the topic of political protest, it is important for our study primarily because of its emphasis on the role of anger. It shows that government punishment might result in feelings of angriness that encourages more people to violate the existing social norm (see also Salimi, 2021, p. 148–151).

Our model, which will be described in the next section, builds on the intersection of two influential traditions in competition policy modeling dating back to the works of Epstein (2002) and Siegel (2011). We integrate them on the basis of the social identity model of collective action, the formalization of which is our main contribution to the existing literature. We also offer the original approach to modeling the multidirectional effects of repression—through anger and risk—on the decision to participate in protest activity.

Model

Fundamental Concepts

Consider a prolonged protest campaign developing according to Granovetter-style dynamics (Granovetter, 1973). Many people share the goals of the protest movement, but prior to a trigger event (which might be a contested election or, say, the self-burning of a man, as it was in a Tunisian case), their motivation is not strong enough to take to the streets. The trigger event may bring to the streets only a relatively small part of the latitude of acceptance (term introduced by McAdam, 1986). However, revealing their preferences heightens the motivations of the other individuals. Thus, more people turn out for the succeeding protest event, further heightening the motivations of the rest. And so on. This bandwagon effect has been the subject of many studies, including those using modeling as a tool for analysis (including Akhremenko & Petrov, 2020).

What we add here to this logic is the idea of dual identity. The key feature of the composition of the protest considered here is that the political opposition consists of two groups (or parties), and each individual has a certain degree of narrow (partisan) identity and a certain degree of broad opposition identity. These components of identity are dynamical variables that depend on repression. If the autocrat aims to repress only one of the groups, then their narrow identity increases, and broad identity decreases. On the other hand, broad repression causes broad identity to rise, while narrow identity may increase or decrease, subject to composition of the local environment. In modeling the identity dynamics, we build to a large extent on empirical findings by Nugent (2020) but posit a few lacking elements.

Then, the dual identity is the multifaceted driver of the protest activities, as shown in Figure 1. Here, we rely largely on SIMCA and the notion of social motive (introduced by Klandermans, 1984 and renamed to “normative” motive by Sturmer & Simon, 2004)). For example, if most of my friends participate in protest activity, I know they expect me to participate as well, and I don't want to disappoint them and/or lose their respect. (In addition to this, repression influences motive for action by fueling anger, see below.)

Figure 1.

Dual identity in the model of protest dynamics.

Of course, repression has a deterring effect along with its influence on identity (and its potential to cause anger). In other words, along with the motive for action described above, each individual also has some motive for inaction. In one case, however, it is equal to zero. This is the case where repression is targeted at the other group. In the case of broad repression or repression targeted at the group to which the person belongs, the motive for inaction is non-zero.

Then, each individual is more or less predisposed toward participation in the long run. This long-term predisposition may vary depending on one’s income, religious affiliation, and more. The measure is a scalar number φ from the segment [−1;0], which we call attitude. We introduce attitude as a negative in order to arrive at the following formula of decision-making:

The individual attends the protest on day t if and only if

φ + M_{action} (t) - M_{i n a c t i o n} (t) > 0

(1)

It follows from this that participants on day t are those individuals whose attitudes φ are large enough: φ>−ψ. Here, ψ is the full motive: ψ = M_action(t) − M_inaction(t). The distribution of attitudes over the latitude of acceptance may be decisive for the success or failure of the protest campaign. In our study, we assume it to be stochastic, nearly uniform. In the empirical literature, there is at least one work supporting the uniform distribution of such a variable (Gonzalez-Bailon et al., 2011).

Following the tradition of considering the logic of recruitment into political participation on the example of a hypothetical activist (McAdam, 1986), imagine an individual having breakfast and weighing motives for participation against motivations for non-participation, while also taking individual-specific long-term predispositions into account. Thus, our approach distinguishes between short-term and long-term factors of protest activity. Short-term factors are those that change over time during the protest campaign, namely, turnout and the severity of repression. Long-term factors, such as disposable income or religious attachment, are constant during the campaign. They are not explicitly represented in the model but are assumed to be aggregated in the individual-specific attitude.

Thus, agents in the model differ by group attachment and attitudes, both of which are constant over time, and also by network environments. The latter has a fixed composition (e.g., one may have seven friends, of which five belong to her own party and two to the other party) but has dynamic levels of participation (maybe none of the friends participate in the first event, but three of them attend the second event, and so on). Agent-level dynamic variables are her narrow identity, broad identity, and participation (0 or 1).

The individual makes her decision as to whether to attend today’s rally based on facts about the previous day, including:

- turnout;

- repression severity and strategy;

- attendance among her friends, taking into account their partisanship.

The whole scheme of decision-making is presented in Figure 2.

Figure 2.

Decision-making.

The model aggregates these decisions from all individuals to obtain the given day's turnout. This turnout feeds back into her next day’s efficacy belief and expected probability of getting exposed to repression as well as to the turnout among her. So the next day and each subsequent day, she makes her decisions, taking into account changes in turnout.

Now, we proceed to a more specific description of the dynamics.

Dynamics of Identity

The general idea of the dynamics of the dual identity embedded into the model is based on empirical findings by Nugent (2020). She conducted a series of laboratory experiments wherein participants immersed in the real political situation in their country (political dissent in Tunisia, 2016) were assigned to one of two fictional opposition groups. In-group and out-group identities were measured as a degree of a respondent’s agreement with statements like “When I talk about the <name of in-group organization>, I would usually say ‘we’ rather than ‘they’”; and “If a story in the media criticized the <name of in-group organization>, I would feel embarrassed.” Prior to measuring the identity, the respondents were also assigned to three treatment groups, which were: informed of broad repression, informed of repression targeted at the in-group; and control group (not informed of any repression). The obtained result was that respondents from the first treatment group exhibited greater out-group identity and lower in-group identity than those from the control group, and vice versa for the second treatment group. The experimental setup, however, considered each respondent separately from the others. That is, the experiment makes no difference between individuals in a local (network) environment consisting of members of their in-group or members of the out-group.

Thus, we propose that if the individual’s network ties are primarily with the opposing party, broad repression causes broad identity to rise (unless it is very high) at the expense of narrow identity. However, if the local environment consists mainly of members of the individual’s own party, the broad repression increases both broad and narrow identities (unless they are very high at the start). In full compliance with Nugent (2020), we assume in our model that repression, targeted at the individual’s party, causes the narrow identity to increase (unless it is high enough at the very start) and the broad identity to decrease (unless it is low enough at the very start).

Specific formulas of the model are provided in the Appendix, while here some key elements of formalization are provided. The broad repression of severity $s_{a b}$ ( $0 \leq s_{a b} \leq 1$ ) drives the dynamics such that,

d_{i, a} (t \to \infty) = \frac{A_{i}}{A_{i} + B_{i}} \max [d_{i, a} (0); s_{a b}] + \frac{B_{i}}{A_{i} + B_{i}} \min [d_{i, a} (0); (1 - s_{a b})]

(2)

d_{i, a b} (t \to \infty) = \max [d_{i, a b} (0); s_{a b}]

(3)

Here, $d_{i, a}$ ( $0 \leq d_{i, a} \leq 1$ ) is narrow (partisan) identity of the i-th individual who is a member of Party A (similarly for members of party B), $d_{i, a b}$ ( $0 \leq d_{i, a b} \leq 1$ ) is broad (opposition) identity of the i-th individual who is a member of Party A, $A_{i} (B_{i})$ —the number of members of Party A (of Party B) in the individual’s local environment. It is put in (2) and (3) such that low-severity broad repression causes identity dynamics only in individuals with small initial identity, whereas severe repression causes dynamics in nearly everyone. Let $s_{a b}$ be high enough, then the individual’s broad identity rises from $d_{i, a b} (0)$ to $s_{a b}$ .

The repression of severity $s_{a}$ ( $0 \leq s_{a} \leq 1$ ) targeted at Party A drives the dynamics such that

d_{i, a} (t \to \infty) = \max [d_{i, a} (0); s_{a}]

(4)

d_{i, a b} (t \to \infty) = \min [d_{i, a b} (0); 1 - s_{a}]

(5)

To sum up, high-severity broad repression causes broad identity to increase, while high-severity targeted repression causes narrow identity to increase. In either case, one of the components of identity increases due to shared experience.

Motive for Action: Anger

It is stated in the model that anger consists of two components. The first is the one that triggered the protest, denoted by $a_{0}$ ( $0 \leq a_{0} \leq 1$ ). It may be caused, for instance, by election fraud, unpopular economic reform or another national-level trigger, so $a_{0}$ is supposed to be the same across all individuals. The second component appears as a backlash against repression. Note that (i) anger is affected only by the severity of repression, not the individual probability of suffering from it; (ii) anger is affected by identity, as prescribed by SIMCA.

So, we have for the anger $a_{i, a}$ , $0 \leq a_{i, a} \leq 1$ of the i-th individual who is a member of Party A in the case of broad repression:

a_{i, a} (t) = 0.5 a_{0} + 0.5 s_{a b} \max (d_{i, a} (t); d_{i, a b} (t)), t \geq 1

(6)

in the case of repression targeted at Party A:

a_{i, a} (t) = 0.5 a_{0} + 0.5 s_{a} \max (d_{i, a} (t); d_{i, a b} (t)), t \geq 1

(7)

in the case of repression of severity

s_{b}

targeted at Party B:

a_{i, a} (t) = 0.5 a_{0} + 0.5 s_{b} d_{i, a b} (t), t \geq 1

(8)

As repression starts at t = 1, we have $a_{i, a} (0) = a_{i, b} (0) = 0.5 a_{0}$ .

The mechanism behind $\max (d_{i, a} (t); d_{i, a b} (t))$ in equations (6) and (7) is as follows. For sake of definiteness, consider the case of broad repression and a hypothetical member of Party A. If, say, her narrow identity is maximum ( $d_{i, a} (t) = 1$ ), it allows the maximum possible effect of a given severity $s_{a b}$ regardless of the value $d_{i, a b} (t)$ of her broad identity. Similarly, if her broad identity is the strongest possible, it doesn’t matter how strong her narrow identity is. In other words, we assume here that it is the greatest component of her identity that conditions her repression-related anger.

Motive for Action: Efficacy Belief

Efficacy belief is the increasing function of both turnout and identity (which is also in accordance with SIMCA). The specification is given in Appendix, while here we demonstrate the graph (Figure 3). The general idea is that if the turnout is low, then the efficacy belief is near zero; if the turnout is high, the efficacy belief is also high. Note that it ranges from 0 to 1.

Figure 3.

Efficacy belief for a member of Party A as a function of turnout. Solid: $\max (d_{i, a}, d_{i, a b}) = 0.7$ , dashed: $\max (d_{i, a}, d_{i, a b}) = 0.5$ .

Motive for Action: Social (Normative) Motivе

As was said earlier, we follow Klandermans (1984) and Sturmer and Simon (2004) by accepting the idea that the local environment can affect behavior. A similar logic was proposed by McAdam (1986) in his consideration of a hypothetical college student who is urged by her friends to attend a rally. McAdam points to the cost of disappointing her friends and losing their respect as a motive for participation if these friends attend the rally. Accordingly, we introduce social motive in our model as dependent on the proportion of the individual’s friends who attended the rally the day before, with identities as coefficients that indicate the importance of these friends. Put simply, the greater the yesterday’s participation among her friends, and her identity, the greater the social motive for action.

Formally, the social motive of a member of Party A is given by:

M_{i, a, n o r m} (t + 1) = \frac{\max (d_{i, a}; d_{i, a b}) T_{i, a} [P a r t i c i p] (t) + d_{i, a b} T_{i, b} [P a r t i c i p] (t)}{T_{i}}

(9)

Here, $T_{i}$ is the number of network ties of the i-th individual; $T_{i, a} [P a r t i c i p] (t)$ ( $T_{i, b} [P a r t i c i p] (t)$ )—the number of members of Party A (of Party B) among the friends of the i-th individual, who attend the protest on day t; $0 \leq M_{i, a, n o r m} (t + 1) \leq 1$ .

Motive for Action: Specification

Motive for action for the i-th individual who is a member of Party A is given by

M_{i, a, a c t i o n} (t + 1) = [1 + \max (d_{i, a}, d_{i, a b})] \frac{a_{i, a} (t) + b_{i, a} (t) + M_{i, a, n o r m} (t + 1)}{6}

(10)

(similarly for the members of Party B). Here, the digit 6 in the denominator normalizes the motive to one so that the motive for action takes values from 0 to 1.

Motive for Inaction

The basic relationships for the motive for inaction are as follows: the higher the turnout, the lower the probability of punishment and thus the lower the motive for inaction; the greater the severity of repression, the greater the motive for inaction. Specifically, the motive for inaction of the member of Party A is given by

M_{a, i n a c t i o n} (t + 1) = {\begin{cases} \exp [- c P (t) / \max [s_{a} (t), s_{a b} (t)]], i f 0 < \max [s_{a} (t), s_{a b} (t)] \leq 1, \\ 0, i f s_{a} (t) = s_{a b} (t) = 0 . \end{cases}

(11)

(similarly for the members of Party B). Here, $P (t)$ is turnout at time t measured as the proportion of all potential protesters. It follows from (11) that $0 < M_{i, a, i n a c t i o n} (t + 1) \leq 1$ if $s_{a} (t) > 0$ or $s_{a b} (t) > 0$ , and $M_{i, a, i n a c t i o n} (t + 1) = 0$ if $s_{a} (t) = s_{a b} (t) = 0$ .

The core of these formulas is the turnout/severity ratio. For a decision-making individual, greater turnouts reduce the risk of being punished. Severity (say, $\max [s_{a} (t), s_{a b} (t)] > 0$ ) being fixed, the motive for inaction is an exponentially decreasing function of turnout: $M_{a, i n a c t i o n} \approx 1$ when $P (t) \approx 0$ and $M_{a, i n a c t i o n} \approx 0$ when $P (t) = 1$ . Turnout being fixed, the motive for inaction is an increasing function of severity.

The parameter c can be treated as $c = 1 / (r i s k a v e r s i o n)$ , where risk aversion is as introduced by Epstein (2002). It should be noted that our logic of introducing the motive for inaction is similar to that of Epstein’s. As his risk aversion ranges from 0 to 1, we take $c \geq 1$ .

Attitude and Decision-Making

The decision-making individual chooses to participate “today” (on day t) if

φ_{i} + M_{i, a c t i o n} (t) - M_{i, i n a c t i o n} (t) > 0

(12)

As said earlier, attitude φ is the measure of long-term predisposition. In our computational experiments, it is supposed to be uniformly distributed. The size of the latitude of acceptance is taken as a unit of population and the distribution of individuals is given by density.

n (φ) = {\begin{cases} 1, - 1 \leq φ \leq 0, \\ 0, o t h e r w i s e . \end{cases}

(13)

In our analytical study, we follow this exact expression. In numerical experiments, the i-th individual is endowed with attitude $φ_{i}$ , which is a random value from $[- 1; 0]$ . This reflects the inherent uncertainty of the situation.

Simulation Method

Computational Model

Based on this mathematical model of political protest mobilization, we implemented a computational model in Python. The implementation of a model written in the framework of object-oriented programming using the Numpy library (Harris et al., 2020) allowed us to vectorize computational operations, thereby increasing the speed of the program script. Several network topologies are implemented in the model using the Networkx library (Hagberg et al., 2008), which generates graphs of various types according to the given parameters: Watts–Strogatz (Watts & Strogatz, 1998), Barabási–Albert (Barabási & Albert, 1999), Erdös–Renyi (Erdös & Rényi, 1959), regular graph, and others.

The model is developed according to the following steps:

1. The first steps are the initialization of the simulation. It includes three stochastic components: the distribution of agents into groups, assigning the attitude value, and generating the network topology. In accordance with a given proportion, agents randomly end up in two groups. In the basic variant (i.e., when an even number of agents and two equally represented groups are given), half of the agents are randomly distributed into the first group and the rest are put into the second. Based on their respective group affiliations, agents form their in- and out-group identities.

2. Each agent then obtains a unique attitude value from the attitude distribution (13).

3. The chosen network topology is initialized.

4. The process of political mobilization. First, the severity of repressions is set (for $t = 0$ , there is no “repression at the previous rally,” so $s_{a} (0) = s_{a b} (0) = 0$ ). Second, identities are updated. Third, in accordance with the given functions, the components of motives for participation and non-participation and the motives themselves are updated. Based on (12), each agent decides whether to participate in the protest and updates their protester or non-protester status.

5. Equilibrium condition is tested. If none of the agents has their status changed during 20 moments, the simulation stops. It stops also if the simulation reaches $t = 100$ . Otherwise, $t \to t + 1$ and go to step 4.

Homophily Accounting

In order to account for homophily, for each of the three network topologies (Watts–Strogatz, Barabási–Albert, and Erdös–Renyi), some modifications were implemented into the original code of the Networkx library (Hagberg et al., 2008).

We introduce the homophily index $H$ to describe how many times ( $P_{H}$ ) the link between agents from the same group is more likely than between agents from different groups. Denote

P_{H} = 1 - \frac{1}{1 + H}

(14)

To generate the Barabási–Albert network with homophily, where the probability $P_{i \leftrightarrow j}$ of joining a “new” vertex i to each of the “old” vertices j depends on both degree $k_{j}$ and partisanships $G_{i}, G_{j}$ , we adjust the standard formulas to get

θ_{j} (i) = {\begin{cases} P_{H} k_{j}, i f G_{i} = G_{j}, \\ (1 - P_{H}) k_{j}, o t h e r w i s e, \end{cases} P_{i \leftrightarrow j} = \frac{θ_{j} (i)}{\sum_{ν = 1}^{m + i} θ_{ν} (i)}

(15)

Similarly, in the case of a random Erdös–Rényi network, we have:

θ_{j} (i) = {\begin{cases} P_{H}, i f G_{i} = G_{j}, \\ 1 - P_{H}, o t h e r w i s e, \end{cases} P_{i \leftrightarrow j} = \frac{θ_{j} (i)}{\sum_{ν = 1}^{N^{2} / 2} θ_{ν} (i)}

(16)

To generate a Watts–Strogatz network with homophily, at the first stage, a ring over n nodes is built in the standard way. Then the connection between the nodes breaks with a certain probability (in our experiments the rewiring probability is taken to be 0.3) and a new connection is created, using probability adjusted with the homophily index:

θ_{j} (i) = {\begin{cases} 0, i f i \leftrightarrow j \\ P_{H}, e l s e i f G_{i} = G_{j}, \\ (1 - P_{H}), o t h e r w i s e, \end{cases} P_{i \leftrightarrow j} = \frac{θ_{j} (i)}{\sum_{ν = 1; ν \neq j}^{N} θ_{ν} (i)}

(17)

Parameters of Simulation

The computational experiment was carried out using the grid search method, during which we considered the following parameter values:

• Severity of repression: 0, 0.2, 0.4, 0.6, 0.8, 1.

• Target of repressions: 0 (general), 1 (directed at the first group), 2 (directed at the second group).

• Watts–Strogatz, Barabási–Albert, Erdös–Renyi, and regular graph network topologies.

• Communication mode: 4, 20, 100.

• Homophily Index: 1, 5, 10.

• For both groups, the initial external identity = 0.2.

• Initial internal identity for both groups = 0.6.

• Initial anger $a_{0}$ = 0.5, 0.75, 1.

• K_IDENT = 0.1.

• K = 6.

• P_ZERO = 0.6.

• c = 4.

Every combination of simulation parameters was run 50 times (a total of 32,400 simulations).

Analytical Study of the Model

For the purpose of our analytical study, we adopt the simplifying assumption of perfect homogeneity. That is, the proportion of members of the parties in the local environment of each individual matches the proportion in the whole latitude of acceptance. Specifically, we assume each party to have 50% of the individuals in the local environment of each individual. Furthermore, the distribution of attitudes is assumed to be perfectly uniform (not stochastic), as prescribed by (13). Repression starts at t = 1 (i.e., it affects the turnout from P(2)) and remains constant).

For large enough values of t, it is possible to derive the equation for the turnout P(t) using these assumptions. It can be shown that the dynamics of identity stops earlier than the dynamics of turnout. Therefore, from a certain moment $t_{0}$ , all identities are constants, and the equation for the dynamics of turnout can be written in the form

P (t + 1) = P (t) + f (P (t)),

where the function

f (P)

depends on the strategy (broad or targeted) and severity of repression. This means that P(t) tends to stable root of the function

f (P)

. One of the typical patterns is shown in Figure 4. (It is noticeable that if P(t) is close to zero, P(t + 1) is formally negative. This is only an artifact of discrete-time modeling similar to numerical (spurious) oscillations that often occur in the discretization of differential equations (see, for example, Xu & Yang, 2021). It does not lead to any practical problems in our case.)

Figure 4.

The function f(P) for targeted and broad repression. Parameters: s = 0.8; $a_{0} = 1; k_{b e l} = 4$ ; $P_{0} = 0.4; c = 4$ ; $d_{i, a} (0) = d_{i, b} (0) = 0.6; d_{i, a b} (0) = d_{i, b a} (0) = 0.2$ for all i.

Consider the case of repression targeted at party A. If $P (t_{0}) < 0.16$ , then $P (t_{0} + 1) < P (t_{0})$ , $P (t_{0} + 2) < P (t_{0} + 1)$ , and so forth, such that $P (t) \to 0$ when $t \to \infty$ . If $P (t_{0}) > 0.16$ , then $P (t_{0} + 1) > P (t_{0})$ , $P (t_{0} + 2) > P (t_{0} + 1)$ , and so forth, such that $P (t) \to 0.45$ when $t \to \infty$ .

In other words, if the protest campaign happens to overcome the threshold $P_{targ, t h r e s h o l d} = 0.16$ , it rises toward $P (\infty) = 0.45$ . If it doesn’t reach that threshold, it fizzles out, such that $P (\infty) = 0$ .

Similarly, the decisive threshold in the case of broad repression is $P_{broad, t h r e s h o l d} = 0.25$ .

Under different values of parameters, $P_{broad, t h r e s h o l d}$ may be less or greater than $P_{targ, t h r e s h o l d}$ ; the same is also true for limits when $t \to \infty$ .

Thus, the value of the threshold depends on the strategy. Of course, it also depends on the severity of repression. The practical problem is that no one actually knows the exact parameters of the model and the distribution of attitudes.

To reflect this uncertainty, our numerical experiments use the stochastic distribution of attitudes. Accordingly, in some experimental settings, one or both strategies of repression yielded a result that $P (t_{0})$ is greater than the threshold in some simulations, and $P (t_{0})$ is lower than the threshold.

If the anger is low enough ( $a_{0} = 0.3$ with the rest of parameters as in Figure 4), then both curves in Figure 4 are completely below the horizontal axis, which means that $P (t) \to 0$ when $t \to \infty$ , that is, the protest fizzles out.

Simulations and Results

According to what was said earlier, each combination of parameters was run 50 times (individuals’ attitudes are stochastic with uniform distribution (13)). Say, the blue dot (0.4; 0.8) in the left top graph in Figure 5 means that in 80% of simulations, the stationary turnout is non-zero. In terms of Figure 4, it would mean that in these 80% simulations, the turnout overcame the threshold and rose to reach the stationary value. The mean of these stationary values across these 80% of simulations is $P (\infty) = 0.45$ , which can be seen from Figure 6 (top left, the point [0.4; 0.45]). In the rest 20% of simulations, the turnout fails to overcome the threshold, and the campaign fizzles out such that $P (\infty) = 0$ .

Figure 5.

The proportion of the simulations in which the turnout at large t (stationary turnout) is non-zero.

Figure 6.

The mean of the turnouts at large t (stationary turnouts).

An important but expected inference from Figure 5 is that anger $a_{0}$ and risk aversion $1 / c$ matter. If the anger is low enough or risk aversion is high enough (Figure 5, all panels except bottom left), broad severe repression suppresses the protest campaign completely and with a guarantee. However, if the anger is high enough and the risk aversion is low enough (Figure 5, bottom left), no level of severity can guarantee the suppression.

Comparing the results for $a_{0} = 1$ (left column of panels in Figure 5) and $a_{0} = 0.5$ (right column), we can see that reducing the initial anger $a_{0}$ softens the collective action in terms of the proportion of the simulations in which the turnout at large t (stationary turnout) is non-zero. The same conclusion in terms of the stationary turnout follows from Figure 6 (compare the middle and bottom rows). This result is in full accordance with the one obtained by Salimi et al. (2022) in relation to the adaptation of new norms.

Moreover, severe broad repression reduces the survivability of protest campaigns but increases the turnout of those campaigns that survive (the curves go down in the bottom left of Figure 5 but go up in bottom left of Figure 6).

Experiments also show that targeted repressions are unable to suppress the protest campaign, which is not surprising because members of the safe party attend the protest without risk of being punished. Moreover, targeted repressions may increase turnout through the mechanism shown in Figures 7 and 8.

Figure 7.

The Dynamics of Participation. Repression: targeted at Party A; $s_{a} = 1$ .

Figure 8.

The scheme of how repression targeted at Party A increases the turnout in Party B and the total turnout.

To illustrate the mechanism, consider hypothetical members of Party A and Party B. As the government commits repression targeted at Party A, it discourages its members from participation through fear (thus leading to a decrease in turnout in Party A), but also causes an increase in their narrow identity. This increase in narrow identity due to targeted repression was empirically shown by Nugent (2020). Note that within a simpler approach (with one-component identity), this increase in identity due to repression was shown in a range of empirical papers, for example, Ayanian and Tausch (2016). Then, according to SIMCA, a stronger narrow identity motivates the members of Party A to attend the protest event. Thus, the turnout in Party A increases. This is observed by members of Party B, who feel more hopeful about the success of the protest campaign. This increase in efficacy belief causes the increase in turnout in Party B.

Figure 9 illustrates the uncertainty as to the turnout. Relatively small stochastic variations in attitudes result in significant variations in turnout. In Figure 9, this refers to the case of targeted repression, but under some other parameters, this uncertainty appears in the case of broad repression as well.

Figure 9.

The Dynamics of Participation. Abscissa: model time, ordinate: the turnout. Each simulation: a pair of curves. Left: total; center: Party A; right: Party B. Red: broad repression. Blue: repression targeted at Party A.

Figure 10 illustrates the influence of attitude distribution on turnout. In this case, because the severity of repression is maximum ( $s_{a b} = 1$ ), the uncertainty is so high that the stationary turnout is either 0 or close to 1. As a measure of the distribution of attitudes, we choose the proportion of individuals with attitudes $φ > - 0.3$ . If it were not stochastic, this proportion would be easy to derive from (13): $\int_{- 0.3}^{0} n (φ) d φ = \int_{- 0.3}^{0} 1 d φ = 0.3 .$

Figure 10.

The influence of attitudes’ distribution on the turnout (broad repression, $s_{a b} = 1$ ).

Due to randomness, it varies (say, for blue dots) approximately from 0.25 to 0.34, and it can be seen that this measure alone has a moderate influence on whether the turnout will be extremely high or zero (bear in mind that other stochastic components of the model are the specific structure of the network and the combination of attitudes with network positions).

Finally, Figure 11 illustrates the role of normative motive. Here, we consider the case of zero repression, so the uncertainty is fairly low. After the first day of the protest, some of the individuals may find that nearly all of their friends (network ties) have attended the rally, while others may find that nearly none of their friends have attended. Accordingly, the normative motive for participation after the first day is strong for some individuals and very weak for others. Green dots in Figure 11 represent the proportion of individuals having the normative motive after the first day greater than 0.3. The pattern obviously shows that this proportion is a relatively strong predictor for the turnout in future periods.

Figure 11.

The influence of the normative motive after the first day of the campaign on the turnout (no repression).

Conclusion and discussion

The major findings can be summarized as follows.

1. Repression can increase uncertainty as to the turnout. That is, a relatively small variation in their attitudes to participate in the protest campaign may result in a significant variation in turnout. The logic can be illustrated with Figure 4. For sake of definiteness, consider the case of broad repression. Due to stochastic character of attitudes in computational experiment, the turnout may exceed or not the threshold (=0.25) found in analytical examination of deterministic model. Then, if it exceeds the threshold, the turnout tends to 0.74; otherwise it tends to zero. Thus, small variation in attitudes leads to significant variation in turnout.

In some situations, the strategy of broad repression increases the uncertainty, while the strategy of targeted repression does not; in other situations, it is vice versa. To make things even more tangled, there seems no simple rule to determine which strategy of repression generates a greater variation in turnout under given parameters. What is clear is that relatively small stochastic factors that can be considered as negligible in a no-repression case appear to be significant when repression is committed. They generate uncertainty, which we consider a plausible explanation for conflicting empirical evidence. As the turnout of the protest campaign in a repressive context is subject to hardly measurable and maybe even unnoticeable variations in parameters, then it is not surprising that empirical studies reach conflicting findings. In other words, our contention is that there is no answer to the question of whether repression increases or reduces turnout. Rather, repression generates uncertainty as to the turnout through making it dependent on small factors that have to be considered stochastic.

2. If anger $a_{0}$ is low enough or risk aversion $1 / c$ is high enough, broad severe repression suppresses the protest campaign completely and with a guarantee. However, if the anger is high enough and the risk aversion is low enough, no level of severity can guarantee the suppression. Moreover, severe broad repression reduces the survivability of protest campaigns but increases the turnout of those campaigns that survive.

3. Targeted repression is unable to suppress the protest campaign. This is not surprising because there is no reason to be inactive for safe party members.

4. If the repression is targeted at one of the parties (Party A), it may result in a greater turnout for this party (than that of the other party). The mechanism is that the repression causes the increase of narrow identity in Party A, which causes the increase of turnout. Moreover, this increase of turnout in Party A may lead to an increase of efficacy belief in Party B and the succeeding increase of turnout in Party B.

5. Homophily affects the turnout of the survived campaigns more than it affects the chance of surviving in the case of targeted repression, and vice versa in the case of broad repression.

The important consideration about psychological antecedents of participation being traditionally overlooked is that the relative comparative importance of anger, efficacy belief, and identification may alter with time. It is possible, for example, that efficacy belief should be taken in the motive for action with a greater coefficient than identity at the early stages of the protest campaign, and vice versa at later stages. The core of the problem here is that most theories and empirical approaches do not consider protest as a prolonged campaign, thus tending to miss out on alterations of any kind that occur during it.

Among the limitations of this study, we’d like to highlight the short-term nature of the considered dynamics. For instance, the short-term benefits for the government that derive from the decrease in turnout tend to result in a longer-term rise in protest movements (Bell & Murdie, 2018; Carey, 2006; Sutton et al., 2014). Severe repression leads to an increase in the likelihood of violent challenges to authorities, such as civil violence and even civil war (Hultquist, 2017). The reliance on force to retain power requires the creation of strong repressive state organizations, which increases the probability of coup d’état (Svolik, 2012). In general, intense repression always increases uncertainty and cannot be considered as a guaranteed way to retain power—this is what previous studies claim, and this is exactly what our computational experiments confirm.

Another limitation of the approach is that decisions considered here are made by the government (which chooses the strategy and severity of repression) and each individual from the opposition, but not by opposition parties that can pursue their own strategy. To remove this limitation, we would have had to employ dynamical or game-theoretical approach.

Supplemental Material

Supplemental Material - Dual Identity in Repressive Contexts: An Agent-Based Model of Protest Dynamics

Supplemental Material for Dual Identity in Repressive Contexts: An Agent-Based Model of Protest Dynamics by Alexander Petrov, Andrei Akhremenko, and Sergey Zheglov in Social Science Computer Review

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Alexander Petrov

Supplemental Material

Supplemental material for this article is available online.

Notes

Author Biograpies

Alexander Petrov is a Doctor of Science in Applied Mathematics and a Leading Researcher at Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences. His research uses mathematical modeling to study collective behavior, including protest movements.

Andrei Akhremenko is a Doctor of Sciences in Political Science and a Leading Research Fellow at the Politics & Psychology Research Laboratory, HSE University, Moscow. He develops agent-based modeling with a focus on political behavior.

Sergey Zheglov is a PhD student at the Doctoral School of Political Science, HSE University, Moscow. He develops a network perspective on the dynamics of protest campaigns.

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